00:01
In this problem, we have two forces, q and p, and i'll just use your, when you list your answer, you list it in kilonutons.
00:09
There are two force factors that does what you use for your units, kiloons, or kips.
00:18
That's not really important here.
00:23
Now, so the goal of the problem is to get the result of the magnitude and direction.
00:31
Now, let's look at q.
00:33
Q is a three -dimensional vector.
00:36
It has a positive y component, but it also has components x and z.
00:42
So what we want to do is find the length of this side of the right triangle, and then break that into its components.
00:50
That's the qxz vector component is itself broken up.
00:59
So let's work on that.
01:02
Qxz.
01:03
This line is in the x z plane qxz qxc q cosign 45 degrees so that will give us this amount here so this then gives me the qx because now once i have this vector i can break it up into its x and z components qx is minus qxy sine 15 degrees qz minus qxy cosine cosine 15 degrees so qxz is our xz vector component and we had to break it up to get individual components.
01:48
Now let's do the same thing for p.
01:50
This line is in the xz plane.
01:53
This has got a negative y component.
01:55
Oh, i should, that would be nice if i gave you the y.
01:58
Qy here is sine 45.
02:04
So we have here q sine 45.
02:08
So we already have got in this side of the right triangle, we need the other.
02:11
And that's the component.
02:13
Okay.
02:15
Now, doing the same thing for p, pxy, or px, z, i should say, px, p, c, p, c, p, cosine, 30 degrees.
02:29
That gives me the vector here, the vector component in the xz plane.
02:34
So this gives me the px, it's equal to px, sine 20 degrees, pz, pxy, cosine, cosine, 20 degrees.
02:48
So there's our x and y components of p and p y is minus p sine 30 degrees.
02:59
So now we have all the components.
03:01
We've just got to add everything up and calculate.
03:04
So the x component of the resultant, qx is px minus q.
03:12
Cosine 45 degrees, sine 15 degrees, plus p cosine 30 degrees, sine 20 degrees minus 8 kiloutons cosine 45 degrees sign 15 degrees 4 kiloons cosine 30 degrees sign 20 degrees and this is equal to minus 0 .279 kilootis that is the x component doing the same thing with y r y qy p y py qy qy py q -sign 45 degrees minus p -sign 30 degrees, 8 kiloons, sign 45 degrees, minus 4 kiloons, sign 30 degrees, and this is 3 .66 kilootts.
04:21
Lastly, we've got to do rz, qz plus pz, minus q, cosine 45 degrees, cosine, cosine, 15, degrees plus p cosine 30 degrees, cosine 20 degrees.
04:41
And putting in our numbers, minus 8 kiloons, cosine 45 degrees, cosine 15 degrees, plus 4 kiloons, cosine 30 degrees, cosine 20 degrees is equal to minus 2 .210...
